Learning for Edge-Weighted Online Bipartite Matching with Robustness Guarantees

Pengfei Li, Jianyi Yang, Shaolei Ren

Keywords: Robustness, online bipartite matching, reinforcement learning

TL;DR: This paper proposes a novel reinforcement learning approach to solve edge-weighted online bipartite matching with robustness guarantees.

Abstract: Many real-world problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but they lack robustness and can perform arbitrarily badly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and good worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judiciously-designed condition to hedge against future uncertainties, decides whether to follow the expert's decision or the RL decision for each online item arrival. We prove that for any $\rho \in [0,1]$, LOMAR is $\rho$-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines.

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